(continued from previous post)
There are certainly applications where a cascode would be highly beneficial. For example in a standard (non-Wilson) current mirror, there are (in general) different voltages across each transistor in the mirror. The Early effect in this situation will cause an error between the reference current and the mirrored current. Cascoding can correct this to a large degree.
Now that is a situation where the current is constant and the voltage varies. But in a linear amplifier, where both the voltage and current are simultaneously changing in accordance with the load line, I'm still not seeing where the Early effect is causing any significant non-linearities. And therefore eliminating the Early effect doesn't seem to confer any great advantages.
There are certainly applications where a cascode would be highly beneficial. For example in a standard (non-Wilson) current mirror, there are (in general) different voltages across each transistor in the mirror. The Early effect in this situation will cause an error between the reference current and the mirrored current. Cascoding can correct this to a large degree.
Now that is a situation where the current is constant and the voltage varies. But in a linear amplifier, where both the voltage and current are simultaneously changing in accordance with the load line, I'm still not seeing where the Early effect is causing any significant non-linearities. And therefore eliminating the Early effect doesn't seem to confer any great advantages.
Charles Hansen said:
You've only addressed linearity here in the context of how constant the current gain is over the dynamic range (which admittedly was Nelson't original argument in connection with the bootstrapped emitter follower). But there's also the issue of how constant the output impedance is (say, for a power amp VAS) over the output voltage swing. Hawksford discusses this issue in his AES article "Reduction of Transistor Slope Impedance Dependent Distortion in Large-Signal Amplifiers". His example uses an amp without global feedback. The simple common emitter amp is worst in this regard, followed by the cascode. He also shows an improved cascode and measurements of distortion comparing the three configurations. At 1kHz, the distortion of the conventional cascode is ten times lower than that of the common emitter amp, and the enhanced cascode is another factor of 3.9 better than that. Feel free to email me for details.
This effect can be demonstrated by spice and by real world testing. Perhaps the compression effect that was mentioned was due to use of overall feedback, and not the use of cascodes. Mr Pass mentioned the lack of compressive effect with cascoding.
Charles Hansen said:
Charles, thanks for those graphs (exel), very clear. It is perhaps also a matter of how much importance one attaches to this. If we disregard the lower part (which I guess is the same as limiting the signal excursion) I see a clear improvement: the pink line is to my eye almost perfectly straight. Is it worth the added expense? For me it would, for you it apparently is not significant. YMMV isn't it?
Jan Didden
Hello All,
A lot of recent postings all tie together, so I am going to *try* to do the same in this response.
First of all, Hawksford's paper provided some interesting (if somewhat dense, as is his style) reading. (I'm still not *exactly* clear what he means by "slope impedance", as that term was apparently coined in a referenced paper by Cherry, and not fully explained in the Hawksford paper.) Here are some of the highlights from Hawksford's paper as it applies to this thread:
1) What he calls an "enhanced cascode" is when the cascode is referenced to the emitter of the input device, as opposed to a standard cascode that is referenced to ground.
He makes a complex argument that the "enhanced cascode" improves the performance because of feedforward mechanisms of error signals. I didn't really take the time to understand what he was trying to say because it seems to me that there is a much simpler explanation. Referencing to the emitter makes the cascode much more "cascode like" (ie, "freezing" the operating points of the input transistor) than does the regular cascode, hence his observed improvement.
2) At low frequencies and with large signal swings, the cascode did improve the measured distortion. In this case, he was using +/- 50 volt rails and running an 80 V p-p output signal. The distortion of the CE stage was 0.4% and the distortion of the cascode was 0.04%.
This reinforces that what janneman and I were saying actually agrees with each other. Looked at from one perspective, the cascode is "10 times more linear". And looked at from another perspective, the CE stage is pretty darn linear already, and that applying a cascode keeps the load line out of the area of the left side of the graph where the "knee" leads to non-linearities at large signal swings. In other words, if the signal swing were reduced by (say) 20%, I'd be willing to bet that the linearity difference would essentially vanish (at low frequencies).
3) The biggest gains to be had from the cascode are from the reduction of non-linear capacitances, which reduces high frequency distortion when using a source generator of finite output impedance. In Hawsksford's circuit, the impedance driving the stage under test was 560 ohms. Hawsksford puts it like this:
"The basic [CE] circuit exhibits a distortion rising with frequency, reaching an unacceptable 1.9% at 50 kHz. This result is a function of the voltage-dependent nature of the device capacitance." (emphasis mine)
As an interesting side note, one of Hawksford equations can be simplified for the case of a zero feedback circuit to:
E = Rg / Zn
where E is the ratio of error signal to primary signal (ie, distortion), Rg is the load resistor that sets the gain, and Zn non-linear output impedance of the transistor (largely composed of non-linear capacitances).
From this equation, it is instantly clear that the distortion of the standard CE circuit is reduced as the load is reduced. This may in large part explain the distortion reduction noted in Pass' white paper where *no* load was used, and in Hawksford's own paper where a relatively high load impedance of 10 kohms was used. In both of these cases, the standard CE circuit was handicapped by running into a relatively large load resistance.
(Now before someone starts an argument about the preceding statement, please note that Hawksford was specifically ignoring non-linearities due to Ie/Vbe variations, and only focusing on non-linearities due to Zn. Distortions due to Ie/Vbe variations will be increased as the load is reduced, so there plainly will be an optimum value of Rg.)
To summarize I would say that, yes, a cascode can provide greater linearity under specific conditions. But from my perspective, saying a "cascode is more linear" is not all that helpful when it comes to improving the art of amplifier design. (Especially considering a parallel thread on this forum the claims that cascodes don't really sound all that great!)
What is far more useful is to understand what the specific mechanisms of distortion reduction are and under what circumstances they apply. Then one has the opportunity to apply various other techniques that can achieve the same advantages, while perhaps avoiding the disadvantages of cascodes.
Best regards,
Charles Hansen
A lot of recent postings all tie together, so I am going to *try* to do the same in this response.
First of all, Hawksford's paper provided some interesting (if somewhat dense, as is his style) reading. (I'm still not *exactly* clear what he means by "slope impedance", as that term was apparently coined in a referenced paper by Cherry, and not fully explained in the Hawksford paper.) Here are some of the highlights from Hawksford's paper as it applies to this thread:
1) What he calls an "enhanced cascode" is when the cascode is referenced to the emitter of the input device, as opposed to a standard cascode that is referenced to ground.
He makes a complex argument that the "enhanced cascode" improves the performance because of feedforward mechanisms of error signals. I didn't really take the time to understand what he was trying to say because it seems to me that there is a much simpler explanation. Referencing to the emitter makes the cascode much more "cascode like" (ie, "freezing" the operating points of the input transistor) than does the regular cascode, hence his observed improvement.
2) At low frequencies and with large signal swings, the cascode did improve the measured distortion. In this case, he was using +/- 50 volt rails and running an 80 V p-p output signal. The distortion of the CE stage was 0.4% and the distortion of the cascode was 0.04%.
This reinforces that what janneman and I were saying actually agrees with each other. Looked at from one perspective, the cascode is "10 times more linear". And looked at from another perspective, the CE stage is pretty darn linear already, and that applying a cascode keeps the load line out of the area of the left side of the graph where the "knee" leads to non-linearities at large signal swings. In other words, if the signal swing were reduced by (say) 20%, I'd be willing to bet that the linearity difference would essentially vanish (at low frequencies).
3) The biggest gains to be had from the cascode are from the reduction of non-linear capacitances, which reduces high frequency distortion when using a source generator of finite output impedance. In Hawsksford's circuit, the impedance driving the stage under test was 560 ohms. Hawsksford puts it like this:
"The basic [CE] circuit exhibits a distortion rising with frequency, reaching an unacceptable 1.9% at 50 kHz. This result is a function of the voltage-dependent nature of the device capacitance." (emphasis mine)
As an interesting side note, one of Hawksford equations can be simplified for the case of a zero feedback circuit to:
E = Rg / Zn
where E is the ratio of error signal to primary signal (ie, distortion), Rg is the load resistor that sets the gain, and Zn non-linear output impedance of the transistor (largely composed of non-linear capacitances).
From this equation, it is instantly clear that the distortion of the standard CE circuit is reduced as the load is reduced. This may in large part explain the distortion reduction noted in Pass' white paper where *no* load was used, and in Hawksford's own paper where a relatively high load impedance of 10 kohms was used. In both of these cases, the standard CE circuit was handicapped by running into a relatively large load resistance.
(Now before someone starts an argument about the preceding statement, please note that Hawksford was specifically ignoring non-linearities due to Ie/Vbe variations, and only focusing on non-linearities due to Zn. Distortions due to Ie/Vbe variations will be increased as the load is reduced, so there plainly will be an optimum value of Rg.)
To summarize I would say that, yes, a cascode can provide greater linearity under specific conditions. But from my perspective, saying a "cascode is more linear" is not all that helpful when it comes to improving the art of amplifier design. (Especially considering a parallel thread on this forum the claims that cascodes don't really sound all that great!)
What is far more useful is to understand what the specific mechanisms of distortion reduction are and under what circumstances they apply. Then one has the opportunity to apply various other techniques that can achieve the same advantages, while perhaps avoiding the disadvantages of cascodes.
Best regards,
Charles Hansen
One more interesting side note from Hawksford's paper. He proposes using a current source across the cascode:
"...where the common-emitter stage operates at a high bias current to improve Ie/Vbe linearity, a bypass current Ix can lower the operating current of the common-base stage."
This is the exact same idea that Pass applied to a cascoded emitter-follower output stage some years later in his patent 5,343,166.
"...where the common-emitter stage operates at a high bias current to improve Ie/Vbe linearity, a bypass current Ix can lower the operating current of the common-base stage."
This is the exact same idea that Pass applied to a cascoded emitter-follower output stage some years later in his patent 5,343,166.
................which Mr.Pass dropped, in his designs, because of its sonic penalty (I believe).😉
Which begs the question, what is the mechenism that causes this (compression effect)?
Regards,
Jam
Which begs the question, what is the mechenism that causes this (compression effect)?
Regards,
Jam
One thing I notice with JFETs is that Vds is reduced (so of course the device curves change). In the case of the Borbely Super Buffer, cascoded Vds for the 1st stage is 2V and 2nd stage 5V. Also, I wonder how things look when you consider complementary circuitry (how do the lines match cascoded v non-cascoded).
JF
JF
Hello Jam,
Actually the patent refers to a way to have the active devices (with low voltage across them) biased into class A, while keeping the cascodes (with high voltage across them) with a much lower standing current to reduce the overall dissipation of the amplifier. As far as I know, Pass has not made any commercial products that embody this patent.
I do remember reading a post somewhere recently where Pass said he stopped using cascodes in the output stage of his amps (like the old Stasis design), but I can't find it now. If anyone is better with the search function than I am, please feel free to let me know where that post was.
As far as a mechanism for a "compression effect", here is a plausible hand-waving one (given for the case of a cascoded follower):
The cascode is driven by the output of the follower. The output of the cascode then goes back to the drain (collector) of the follower. Please note that there are two stages of delay between the original input signal and the action of the cascode:
1) Delay between the input to the follower and the output from the follower.
2) Delay between the input to the cascode and the output of the cascode.
So we can see that if the input voltage were to go up, the voltage applied to the follower's drain (collector) would also go up, but only after a slight time delay. Perhaps it is this time delay that causes the "compression effect" you have noted.
Best regards,
Charles Hansen
Actually the patent refers to a way to have the active devices (with low voltage across them) biased into class A, while keeping the cascodes (with high voltage across them) with a much lower standing current to reduce the overall dissipation of the amplifier. As far as I know, Pass has not made any commercial products that embody this patent.
I do remember reading a post somewhere recently where Pass said he stopped using cascodes in the output stage of his amps (like the old Stasis design), but I can't find it now. If anyone is better with the search function than I am, please feel free to let me know where that post was.
As far as a mechanism for a "compression effect", here is a plausible hand-waving one (given for the case of a cascoded follower):
The cascode is driven by the output of the follower. The output of the cascode then goes back to the drain (collector) of the follower. Please note that there are two stages of delay between the original input signal and the action of the cascode:
1) Delay between the input to the follower and the output from the follower.
2) Delay between the input to the cascode and the output of the cascode.
So we can see that if the input voltage were to go up, the voltage applied to the follower's drain (collector) would also go up, but only after a slight time delay. Perhaps it is this time delay that causes the "compression effect" you have noted.
Best regards,
Charles Hansen
Charles,
That makes a lot of sense. Which lends support to the idea that cascodes should be biased with reference to ground but in this case would severly limit output swing.
Regards,
Jam
That makes a lot of sense. Which lends support to the idea that cascodes should be biased with reference to ground but in this case would severly limit output swing.
Regards,
Jam
BTDT
"...where the common-emitter stage operates at a high bias current to improve Ie/Vbe linearity, a bypass current Ix can lower the operating current of the common-base stage."
It's been done for decades............. it's called a folded cascode. Academics seem to often the last ones to know.
"Distortions due to Ie/Vbe variations will be increased as the load is reduced, so there plainly will be an optimum value of Rg."
For a given change in Vbe the opposite is true last time I heard........
"...where the common-emitter stage operates at a high bias current to improve Ie/Vbe linearity, a bypass current Ix can lower the operating current of the common-base stage."
It's been done for decades............. it's called a folded cascode. Academics seem to often the last ones to know.
"Distortions due to Ie/Vbe variations will be increased as the load is reduced, so there plainly will be an optimum value of Rg."
For a given change in Vbe the opposite is true last time I heard........
Well, I went and got a patent on it anyway. 😉
In reference to the apparent compression using cascoding on
an emitter follower output stage, this was of course an
anecdotal case, and can't be regarded as general until more
information is on the table.
The conclusion was reached simply by listening, and was not
indicated by measurements. In this business, the ears win.
As to why, an even simpler hand waving kind of explanation
might be "There's more crap in series with the power signal path
- of course it reduces dynamics."
😎
In reference to the apparent compression using cascoding on
an emitter follower output stage, this was of course an
anecdotal case, and can't be regarded as general until more
information is on the table.
The conclusion was reached simply by listening, and was not
indicated by measurements. In this business, the ears win.
As to why, an even simpler hand waving kind of explanation
might be "There's more crap in series with the power signal path
- of course it reduces dynamics."
😎
Re: BTDT
Fred, I noted that as well. I think, knowing Hawksford and the way the paper reads, it would be sensible to assume he meant..." as the load resistance Rg is reduced..". Let's forgive him, shall we?
Jan Didden
Fred Dieckmann said:
Fred, I noted that as well. I think, knowing Hawksford and the way the paper reads, it would be sensible to assume he meant..." as the load resistance Rg is reduced..". Let's forgive him, shall we?
Jan Didden
Re: Re: BTDT
Well actually Fred was quoting me, not Hawksford. You did cipher my meaning. Is your forgiveness of the blanket sort? 🙂
janneman said:
Well actually Fred was quoting me, not Hawksford. You did cipher my meaning. Is your forgiveness of the blanket sort? 🙂
Forgive what
Lets see............ I want to get something straight technically and I'm picking on some one I never met😕
Coming up with the idea for folded cascode 20 years after it has been widely used in even op amps .........
It's just sad 
"Is your forgiveness of the blanket sort?"
I was thinking of selling indulgences like the Catholic church did a few centuries ago, but that would be wrong!
Lets see............ I want to get something straight technically and I'm picking on some one I never met😕
Coming up with the idea for folded cascode 20 years after it has been widely used in even op amps .........
It's just sad "Is your forgiveness of the blanket sort?"
I was thinking of selling indulgences like the Catholic church did a few centuries ago, but that would be wrong!
Hello Fred,
I forgive you, even if you don't forgive me! 🙂
Regarding the circuit Hawksford was talking about, it is not a folded cascode. His twist is the current source labeled "Ix" that bridges the two inner transistors. This allows the two input transistors to be biased well into class A, while keeping the dissipation down in the two cascode transistors.
Cheers,
Charles Hansen
I forgive you, even if you don't forgive me! 🙂
Regarding the circuit Hawksford was talking about, it is not a folded cascode. His twist is the current source labeled "Ix" that bridges the two inner transistors. This allows the two input transistors to be biased well into class A, while keeping the dissipation down in the two cascode transistors.
Cheers,
Charles Hansen
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